Information Flow and Graph Structure in On-Line Social Networks Jon Kleinberg Cornell University Including joint work with Lada Adamic, Ashton Anderson, Lars Backstrom, Flavio Chierichetti, Justin Cheng, Cristian Danescu-Niculescu-Mizil, Lillian Lee, Jure Leskovec, David Liben-Nowell, Mitul Tiwari, and Johan Ugander.
Two Metaphors for the Web On-line networks are balanced between two metaphors. The library: pages, hyperlinks, associations. The crowd: real-time awareness, memes, contagion.
Wholly new forms of encyclopedias will appear, ready made with a mesh of associative trails running through them ... There is a new profession of trail blazers, those who find delight in the task of establishing useful trails through the enormous mass of the common record. — Vannevar Bush, As We May Think , 1945
Wholly new forms of encyclopedias will appear, ready made with a mesh of associative trails running through them ... There is a new profession of trail blazers, those who find delight in the task of establishing useful trails through the enormous mass of the common record. — Vannevar Bush, As We May Think , 1945 .... radio and the printed page seemed to have only negligible effects on actual vote decisions .... When [people] were asked what had contributed to their decision, their answer was: other people. — Elihu Katz and Paul Lazarsfeld, . Personal Influence , 1955 Diffusion of innovations: Ryan-Gross 43, Lazarsfeld et al 44, Coleman et al 66, Friedkin-Johnsen 90, Blume 93, Ellison 93, Domingos-Richardson 01, Kempe et al 03
Portion of a Facebook visualization, 2010 What are on-line social networks accomplishing for their users? 1 Transport mechanism for information, opinions, behaviors. 2 Assistance for maintaining social ties over time.
Social Transport of Information Dear All, The US Congress has authorised the President of the US to go to war against Iraq. Please consider this an urgent request. UN Petition for Peace: [...] Please COPY (rather than Forward) this e-mail in a new message, sign at the end of the list, and send it to all the people whom you know. If you receive this list with more than 500 names signed, please send a copy of the message to: usa@un.int president@whitehouse.gov Chain-letter petitions as “tracers” through global social network [LibenNowell-Kleinberg]
Social Transport of Information Analyses of information propagation in many domains. Natural tree structure: w acquires from v = ⇒ v is parent of w . Links via blog posts [Adar et al 2004, Gruhl et al 2004] Product recommendations [Leskovec et al 2006] Chain-letter petitions [LibenNowell-Kleinberg 2008, Golub-Jackson 2010] Quoted phrases through news, blogs [Leskovec-Backstrom-Kleinberg 09] Facebook copy-paste and photo memes [Adamic et al 12, Cheng et al 14] Cascading invitations to join new platforms [Anderson et al 2015]
Social Transport of Information A first issue: networks have very low diameter, but trees are deep. [Kleinberg-LibenNowell, Iribarren-Moro, Golub-Jackson] Selective sharing producing a sparse subgraph. Particular role for strong ties. Large heterogeneity in rate of node response. cf. literature on shortest paths with random edge lengths [Frieze 1982, Hassin 1985, Psaraftis-Tsitsiklis 1992] Open: A reasonable model of tree depth with provable guarantees.
Adding Recurrence as a Phenomenon p 0 p 1 # Reshares h b 0 b 1 w r t Roughly 30-40% of Facebook image/video memes recur. [Cheng-Adamic-Kleinberg-Leskovec 2016] Can define recurrence by inferring an on/off state transition in an underlying generative model for volume, or by simple thresholding.
Outbreaks of Moderate Size Conditioned on size of first outbreak, expected number of future outbreaks maximized for moderate-sized cascades. Consistent with a simple probabilistic contagion model: Meme appears spontaneously at random nodes at randomly spaced times. Nodes accept meme from neighbors with fixed probability p . Nodes have reduced probability p ′ < p after first exposure (a variant of SIR epidemic model). Giant cascades exhaust population in first outbreak; small cascades never get going.
The Effect of Language Dear All, The US Congress has authorised the President of the US to go to war against Iraq. Please consider this an urgent request. UN Petition for Peace: [...] Please COPY (rather than Forward) this e-mail in a new message, sign at the end of the list, and send it to all the people whom you know. If you receive this list with more than 500 names signed, please send a copy of the message to: usa@un.int president@whitehouse.gov Does the language used help us predict the success of the meme? e.g. [Hovland et al 1953; Nickerson-Rogers 2010; Milkman-Berger 2012]
Same user tweeting same URL with different text, within 12 hours. [Tan-Lee-Pang 2014] First post vs. second post gives essentially no predictive value. Are there useful features in the language of the tweet? Human performance 61.3%; algorithmic performance 65.6% Key features included probability of tweet under language models built from: universe of Tweets; user’s past tweets; successful tweets.
Viral Text Similar algorithmic performance on a corpus of movie quotes. [DanescuNiculescuMizil-Cheng-Kleinberg-Lee 2012] Compare pairs of movie lines of approx. same length, spoken by same character in same scene of same movie. Algorithmic performance 64%; now human performance 75%. Stormtrooper: Let me see your identification. Obi-Wan: You don’t need to see his identification. Stormtrooper: We don’t need to see his identification. Obi-Wan: These aren’t the droids you’re looking for. Stormtrooper: These aren’t the droids we’re looking for. Obi-Wan: He can go about his business. Stormtrooper: You can go about your business.
Meme Ecology Mutation of textual memes as they travel from source to source. Used for phrase clustering in Leskovec-Backstrom-Kleinberg 2009 More extensive analysis by Simmons-Adamic-Adar 2011 Genetic analogy for memes: beginning of a formalization? Fitness functions Mutation mechanisms Preservation of “functional” elements
Portion of a Facebook visualization, 2010 What are on-line social networks accomplishing for their users? 1 Transport mechanism for information, opinions, behaviors. 2 Assistance for maintaining social ties over time.
Marlow-Byron-Lento-Rosenn 2009 One person’s network neighborhood. Think of Facebook not as a billion-node network, but instead as a collection of a billion (relatively dense) small networks. [Ugander-Backstrom-Kleinberg 2013]
A Baseline Model G n , p : place n nodes; connect each pair independently with probability p . Erd¨ os-R´ enyi 1960, Gilbert 1959 Deficiencies with the G n , p model: Doesn’t produce nodes with enormous numbers of neighbors. (More a problem for Web graphs than social networks.) Real social networks are rich in triangles: triadic closure.
A Baseline Model G n , p : place n nodes; connect each pair independently with probability p . Erd¨ os-R´ enyi 1960, Gilbert 1959 Deficiencies with the G n , p model: Doesn’t produce nodes with enormous numbers of neighbors. (More a problem for Web graphs than social networks.) Real social networks are rich in triangles: triadic closure.
A Baseline Model G n , p : place n nodes; connect each pair independently with probability p . Erd¨ os-R´ enyi 1960, Gilbert 1959 Deficiencies with the G n , p model: Doesn’t produce nodes with enormous numbers of neighbors. (More a problem for Web graphs than social networks.) Real social networks are rich in triangles: triadic closure.
Characterizing neighborhoods Describe neighborhood G by vector of subgraph frequencies: For small k , and each k -node graph H , let f G ( H ) = frac. of k -node sets inducing H . Triad census: Davis-Leinhardt 71 Network motifs: Milo et al 02 Frequent subgraph mining: Yan-Han 02, Kuramochi-Karypis 04 Subgraph density, homomorphisms: Borgs-Chayes-Lov´ asz-S´ os-Vesztergombi, Razborov 07 Characterizing neighborhoods: Ugander-Backstrom-Kleinberg 13
Characterizing neighborhoods Describe neighborhood G by vector of subgraph frequencies: For small k , and each k -node graph H , let f G ( H ) = frac. of k -node sets inducing H . Triad census: Davis-Leinhardt 71 Network motifs: Milo et al 02 Frequent subgraph mining: Yan-Han 02, Kuramochi-Karypis 04 Subgraph density, homomorphisms: Borgs-Chayes-Lov´ asz-S´ os-Vesztergombi, Razborov 07 Characterizing neighborhoods: Ugander-Backstrom-Kleinberg 13
The geography of Facebook neighborhoods Axes: triad frequencies “Coastlines:” freq of 1-edge triad is ≤ 3 / 4. Unpopulated areas: freq of 2-edge triad never close to 3/4 in real life. Full feasible region contains hard extremal graph theory questions [Razborov 2007]. G n , p is the “backbone” that runs through the points. With deviations based on triadic closure and clustering.
The geography of Facebook neighborhoods Axes: triad frequencies “Coastlines:” freq of 1-edge triad is ≤ 3 / 4. Unpopulated areas: freq of 2-edge triad never close to 3/4 in real life. Full feasible region contains hard extremal graph theory questions [Razborov 2007]. G n , p is the “backbone” that runs through the points. With deviations based on triadic closure and clustering.
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